Analytical and Numerical Approaches to Mathematical Relativity by J?rg Frauendie

Description: Analytical and Numerical Approaches to Mathematical Relativity by Jörg Frauendiener, Roger Penrose, Domenico J.W. Giulini, Volker Perlick General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This title collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description The general theory of relativity, as formulated by Albert Einstein in 1915, provided an astoundingly original perspective on the physical nature of gr- itation, showing that it could be understood as a feature of a curvature in the four-dimensional continuum of space-time. Now, some 90 years later, this extraordinary theory stands in superb agreement with observation, prov- ing a profound accord between the theory and the actual physical behavior of astronomical bodies, which sometimes attains a phenomenal precision (in one case to about one part in one hundred million million, where several d- ferent non-Newtonian e?ects, including the emission of gravitational waves, are convincingly con?rmed). Einsteins tentative introduction, in 1917, of an additional term in his equations, speci?ed by a "cosmological constant", - pearsnowtobeobservationallydemanded,andwiththistermincluded,there is no discrepancy known between Einsteins theory and classical dynamical behavior, from meteors to matter distributions at the largest cosmological scales. One of Einsteins famous theoretical predictions that light is bent in a gravitational ?eld (which had been only roughly con?rmed by Eddingtons solareclipsemeasurementsattheIslandofPrincipein1919,butwhichisnow very well established) has become an important tool in observational cosm- ogy, where gravitational lensing now provides a unique and direct means of measuring the mass of very distant objects. Back Cover Today, general relativity rates among the most accurately tested fundamental theories in all of physics. However, deficiencies in our mathematical and conceptual understanding still exist, and these partly hamper further progress. For this reason alone, but no less important from the point of view that a theory-based prediction should be regarded as no better than ones own structural understanding of the underlying theory, one should undertake serious investigations into the corresponding mathematical issues. This book contains a representative collection of surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods. This book addresses graduate students and specialist researchers alike. Table of Contents Differential Geometry and Differential Topology.- A Personal Perspective on Global Lorentzian Geometry.- The Space of Null Geodesics (and a New Causal Boundary).- Some Variational Problems in Semi-Riemannian Geometry.- On the Geometry of pp-Wave Type Spacetimes.- Analytical Methods and Differential Equations.- Concepts of Hyperbolicity and Relativistic Continuum Mechanics.- Elliptic Systems.- Mathematical Properties of Cosmological Models with Accelerated Expansion.- The Poincaré Structure and the Centre-of-Mass of Asymptotically Flat Spacetimes.- Numerical Methods.- Computer Simulation – a Tool for Mathematical Relativity – and Vice Versa.- On Boundary Conditions for the Einstein Equations.- Recent Analytical and Numerical Techniques Applied to the Einstein Equations.- Some Mathematical Problems in Numerical Relativity. Review From the reviews:"The 319th Wilhelm-and-Else-Heraeus Seminar Mathematical Relativity: New Ideas and Developments took place in March 2004. Twelve of the invited speakers have expanded their one hour talks into the papers appearing in this volume … . volume contains a wealth of diverse, fascinating material which needs to be perused by research students and others new to this field. Many will wish to buy it, but even if you do not, make sure your institutions library purchases a copy!" (John M Stewart, Classical and Quantum Gravity, Issue 24, 2007) Long Description The general theory of relativity, as formulated by Albert Einstein in 1915, provided an astoundingly original perspective on the physical nature of gr- itation, showing that it could be understood as a feature of a curvature in the four-dimensional continuum of space-time. Now, some 90 years later, this extraordinary theory stands in superb agreement with observation, prov- ing a profound accord between the theory and the actual physical behavior of astronomical bodies, which sometimes attains a phenomenal precision (in one case to about one part in one hundred million million, where several d- ferent non-Newtonian eects, including the emission of gravitational waves, are convincingly conrmed). Einsteins tentative introduction, in 1917, of an additional term in his equations, specied by a "cosmological constant", - pearsnowtobeobservationallydemanded,andwiththistermincluded,there is no discrepancy known between Einsteins theory and classical dynamical behavior, from meteors to matter distributions at the largest cosmological scales. One of Einsteins famous theoretical predictions that light is bent in a gravitational ?eld (which had been only roughly conrmed by Eddingtons solareclipsemeasurementsattheIslandofPrincipein1919,butwhichisnow very well established) has become an important tool in observational cosm- ogy, where gravitational lensing now provides a unique and direct means of measuring the mass of very distant objects. Review Text From the reviews: "The 319th Wilhelm-and-Else-Heraeus Seminar a?Mathematical Relativity: New Ideas and Developmentsa? took place in March 2004. Twelve of the invited speakers have expanded their one hour talks into the papers appearing in this volume a? . volume contains a wealth of diverse, fascinating material which needs to be perused by research students and others new to this field. Many will wish to buy it, but even if you do not, make sure your institutionas library purchases a copy!" (John M Stewart, Classical and Quantum Gravity, Issue 24, 2007) Review Quote From the reviews:"The 319th Wilhelm-and-Else-Heraeus Seminar Mathematical Relativity: New Ideas and Developments took place in March 2004. Twelve of the invited speakers have expanded their one hour talks into the papers appearing in this volume … . volume contains a wealth of diverse, fascinating material which needs to be perused by research students and others new to this field. Many will wish to buy it, but even if you do not, make sure your institutions library purchases a copy!" (John M Stewart, Classical and Quantum Gravity, Issue 24, 2007) Feature Reviews accurately tested fundeamental theory, Includes surveys by experts in mathematical relativity Includes differential geometry and differential topology, analytical methods and differential equations, and numerical methods Details ISBN3540310274 Short Title ANALYTICAL & NUMERICAL APPROAC Series Lecture Notes in Physics Language English ISBN-10 3540310274 ISBN-13 9783540310273 Media Book Format Hardcover Series Number 692 Year 2006 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany Edited by Jörg Frauendiener DEWEY 530.1986 Pages 281 Edition 2006th DOI 10.1604/9783540310273 Author Volker Perlick Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2006 ed. Publication Date 2006-03-09 Alternative 9783642068195 Audience Professional & Vocational Illustrations XVII, 281 p. 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